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Theorem jcab 863
Description: Distributive law for implication over conjunction. Compare Theorem *4.76 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 27-Nov-2013.)
Assertion
Ref Expression
jcab

Proof of Theorem jcab
StepHypRef Expression
1 simpl 457 . . . 4
21imim2i 14 . . 3
3 simpr 461 . . . 4
43imim2i 14 . . 3
52, 4jca 532 . 2
6 pm3.43 862 . 2
75, 6impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369
This theorem is referenced by:  ordi  864  pm4.76  866  pm5.44  911  2mo2  2372  2eu4OLD  2381  ssconb  3636  ssin  3719  tfr3  7087  isprm2  14225  lgsquad2lem2  23634  ostthlem2  23813  2reu4a  32194  pclclN  35615  bj-ifbibib  37721
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
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